A **test statistic** can be used to confirm or reject the null hypotheses in a Hypothesis test. The test statistic compares the data you collected from an experiment or survey to what you would expect if the null hypotheses were true.

The test statistic is the number that indicates how far your test results are from those of the null hypotheses. Let’s say, for example, that you believe Drug X can cure warts. The null hypothesis states that approximately 30% of warts disappear on their own. You run a clinical study and discover that 57% of your patients have been cured by drug X. This is a significant outcome. Does the drug actually work? Is this 57% result a fluke? These questions can be answered by using a test statistic and a probability value. (P-value).

### What is a test statistic?

A test statistic measures how closely your sample matches the null hypothesis for a hypotheses test. The test statistic calculates your sample data into a single number which quantifies the amount your sample differs from the null hypotheses. Test statistic values that are more extreme indicate larger differences between the sample data and the null hypothesis.

You can use a test statistic to evaluate statistical significance by comparing it with a critical value or using it to calculate the data. Statisticians called the hypothesis tests after test statistics because that’s the quantity the tests evaluate. The t-test evaluates t values, the F-test evaluates F values, and the chi-square tests are based on chi-square values.

This post will teach you how to calculate test statistics and interpret them. You’ll also learn about the p-value and critical value methods for evaluating statistical significance.

The central tendency and variation are different based on which statistical test you use. It’s important to understand the difference between a null hypothesis and an alternative one.

- Null Hypothesis This hypothesis states that the means of both sample groups are equal. The goal of statistical tests is to reject or prove the null hypotheses.
- Alternative hypothesis. Alternative hypotheses suggest that there are significant differences between the two samples, and the variations within the groups lead to unequal means. When you reach an alternative hypothesis through statistical analysis, this can be a sign that the null hypothesis is not true.

### Test Statistics: Interpretation

Test statistics are not unitless. They can be difficult to interpret by themselves because of this. You already know that they will evaluate the degree to which your data are in agreement with the null hypotheses. Your data will be so out of agreement with the null hypotheses if your test statistic is extreme that you can reject this and conclude your results are statistically important if your test statistic is extreme. How does this translate into specific values for your test statistic? What is the limit?

The null value is a t-value of zero. How far away from zero does your t value need to be for it to be statistically meaningful? Does 1 suffice? 2? 3? What does your t value mean? We know in this case that the sample means does not equal the null values, but is the value exceptional? The dividing line can be different depending on the sample size, study design, and other factors.

The other test statistics also have similar questions.

In order to interpret the individual values of test statistics, we must place them within a larger context. Let me introduce to you the sampling distributions of test statistics.